Nahid V - "Fallen tree"

I started writing this post in an attempt to capture certain ideas about how value is projected, and how those projections can be misconstrued. Halfway there I began to realize that I was instead creating a kind of embedded language for discussing the perceptions of actions in general. This post will, therefore, focus on the idea of action perception, with some examples. I will soon write another post to get back to the original topic viewed with the help of the ideas discussed here.

Let’s talk a little about the title.

Most of the interactions in our day-to-day lives are just that - actions. These actions occur between people, groups, objects, or are self-inflicted. We mostly limit our conversations about these actions to remarks about their circumstances, and the details involved in their construction and execution. However, if a tree falls in a forest, and it is not perceived, does it still make a sound? It is important to keep in mind the contexts and interpretations of the perceptions of actions that occur.

Index ( diagrams* )

• Action
• Observation
• Perception
• Inaction
• Parties
• Self-Action
• One-Party Problem *
• Analysis
• One-Party Problem Analysis *
• Mis-Perception
• Two-Party Problem *
• Theory of Mind
• Bodies
• One-Body Problem *
• Group-Action
• Group-Perceptions
• Two Two-Party Bodies Problem *
• What’s Missing?
• What’s Next?
• Links
• Notes
• Appendix

Action

An action is an objective real-world event that occurs between concrete or abstract entities within in the world.

Bob pours himself a glass of water.

Observation

An observation is the concrete phenomenon of the receipt of information by an entity pertaining to an action.

Alice hears Bob pour the water from another room.

Perception

Perception is the witnessing-entity’s understanding of the information pertaining to the action that it observed.

Alice understands that that someone in the other room poured a liquid into a vessel.

Inaction

The simplest form of action is no action at all. It exhibits no observable phenomenon aside from a lack of observations. Still, although there are no observations to be made, there are still an infinity of perceptions of inaction that are possible through the interpretation of the meaning of the non-event.

There could be a wealth of content to be written about inaction, but I won’t touch on it any further here. Instead focusing on singular observable actions.

Parties

Although actions cab be described as occurring between abstract entities, the simplest type of entity is the “Party”. A party is a single actor such as a person, or animal. Parties can perform and receive actions, but they can also observe and perceive actions. Parties can also go further and extend thought processes further than simple interpretations of the concrete.

A simple diagram of three parties can be shown as follows:

Alice     Bob

          Carol

Self-Action

The simplest concrete action is self-action. This is because it requires only one entity to perform and receive the action. The same entity can observe and perceive the action, and their thoughts need pertain only to themselves.

An example of a self-action could be Bob’s refreshment from earlier:

Bob pours himself a glass of water.

One-Party Problem

The previous example of Bob’s refreshment (sans witnesses) is a variant of what I call “The One-Party Problem”. A Party performs an Action upon itself. It observes that action, and perceives it. Although this seems to be a contrived and solipsistic construction of an example, there is still something to be gained by examining the forces at play in the scenario.

• Are actions in this scenario important?
• Can the party involved form an objective interpretation of the events that unfolded?
• How linked are action, observation, and perception?
• Is the party merely perceiving the scenario, or also transformed by those perceptions?

And so, the “Perceptive-Graph” for the One-Party Problem:

   /-----+
   :     : AP1
   :     v
Party 1 ---+
   ^       |
   |   A   |
   |       |
   \-------+

• One party acts on itself
• “Party 1” represents the party
• “A” represents the action
• There is an implicit group present containing “Party 1”, however, this doesn’t matter for single parties
• “AP1” represents “Party 1”s perception of action “A”

Currently AP1 is explicitly drawn on the graph, however, there are such arrows from every party to every action, so we may leave them out of the diagrams and refer to them via the convention (Action)-(Party). These can then be referenced and discussed in tabular form.

The diagram then simply becomes an Action-Entity graph. In this example:

Party 1 ---+
   ^       |
   |   A   |
   |       |
   \-------+

Analysis

For any particular Action-Entity graph an analysis can be performed. This takes the form of a series of levels of descriptions. With the items being described becoming more abstract with each level.

The levels begin as follows:

After the initial action-entity diagram has been constructed, each successive level of abstraction can be generated by taking the cross-product of the previous level of abstraction with the set of entities. For example, each party perceives all actions, and each party also models all such perceptions. For scenarios composed of many entities and actions, this can lead to a combinatorial explosion of descriptions. However, if you refer to entities purely through abstract circumstance, then you will find that many of these descriptions will be identical, and their implications only need to be considered once.

There is no limit to how many levels of abstraction can be analysed, but three should be sufficient for most practical discussion.

Here is analysis of the One-Party Problem

Analysis of the Abstract One Party Problem

Party 1 ---+
   ^       |
   |   A   |
   |       |
   \-------+

Analysis of

Parties’ Interpretation of Actions

Mis-Perception

Where there is perception, as distinct from observation, there is always mis-perception. An understanding of events that does not reflect reality. In the analysis of abstract entity-action scenarios this is not terribly interesting, however, in concrete scenarios it is very important. The mis-understanding of various parties should be derived so that their future behaviour can be better predicted, and so that the models of their understanding by other parties can be improved.

Two-Party Problem

Here, I present the two-party problem. Two concrete entities with a single action from one to the other. No self-actions are presented as, while these are very interesting, they don’t add anything new to the scenario.

          A
Party 1 ----> Party 2

Analysis of

Parties’ Interpretation of Actions

This scenario provides one of the simplest, yet non-trivial diagrams in terms of the actions and entities involved. While it is extraordinarily simple, I believe that most situational analysis attempts to reduce any complexity down to this model. This is deficient in many situations and can only provide a cursory and limited understanding of the perceptions, specifically mis-perceptions as well as how they relate to an objective truth, in terms of individuals, and especially groups.

Theory of Mind

Once multiple parties are involved, it becomes useful to begin exploring the concept of “Theory of Mind (ToM).” Theory of Mind as a concept has been used extensively in psychological and animal-behaviour research in order to understand the nuances and sophistication of a subject’s mental models of other actors. Tests for the presence of ToM in subjects include observing food-hiding behaviours in the company of other animals, etc. Theory of Mind comprises the third level of action-entity analysis, forming the cross-product of perceptions and entities.

For example, the One-Party Problem yields not just self-perception, but also an inner theory of the party’s own mind:

This is all very self-obsessed, so let’s view ToM in the context of the Two-Party Problem (with the diagram again for reference):

          A
Party 1 ----> Party 2

I’m sure that as you read the descriptions in the table above you feel frustrated at just how limited the English language is at describing multi-layered entity interactions in an abstract fashion. However, it is not good enough to simply use names and make each entity explicit in the descriptions, as the relativistic form that the descriptions take is what allows them to be compared for equality.

That being said, let’s put Theory of Mind aside for now, it being enough that the concept is codified as a level, so that it can be referred to later.

Bodies

So far, we have looked at simple scenarios involving multiple parties, and multiple levels of interpretation of the actions involved between those parties. From here, it’s easy to imagine scenarios that you’re already familiar with, and how this framework may make it easier to describe what is occurring, however, even with a plethora more parties and actions involved, there is still a crucial concept that must be added before any greater numeric complexity is accrued. This concept is the notion of groups, or bodies. It is what allows us to say “we”, “the opposition”, “our allies”, etc.

There is a huge degree of nuance involved with the concept of groups, but for simplicities sake, we’ll simply say that a party is either in a group, or isn’t. Our examples will use groups that do not overlap, and that don’t contain sub-groups. A group is not a party, but it is an entity.

The Two-Party One-Body Problem

           Body 1
      +--------------+
      |              |
+-------- Party 1    |
| B   |              |
\---> |      | A     |
      |      |       |
+-----|      V       |----+
| C   |              |  D |
\-------> Party 2    | <--/
      |              |
      +--------------+

Analysis of

Interpretation of Actions

The first impression we get from this table is that there are quite a few more rows than last time. The first example had one descriptive row, the second - four. And now, this slightly more involved example has 12.

The number of rows follows a formula: N = A * E ^ (L - 1).

In this case, 12 = 4 * 3 ^ (2 - 1).

N = 12         = Number of Descriptions
A =  4         = Actions
E =  3 = B + P = Entities
B =  1         = Bodies
P =  2         = Parties
L =  2 = Level = "Description of Perception"

We also see the first occurrence of a descriptive equality. The perceptions DP1 = DP2 up to description. No matter which party is observing it, the group acting upon itself is described the same way. So in actual fact, the formula should really take this into account. The number we’ve derived N is the upper bound in the number of descriptions, however, once duplicates are removed, the real number may be lower. Finding a formula for that number is left as an exercise to the reader.

There are some other phenomenon that appear for the first time in this scenario.

Group-Action

Here is where the first non-concrete diagrammatic representation creeps in. Clearly, there is no single instance of “group-action” in the real world, however, we have drawn an arrow representing an action, from the group to various entities, including the group itself. Weather or not this is permissible is left up to the drafter of the diagram that represents any particular scenario. I include the representation in order to capture the idea of multi-action aggregates, or notional perception of implied aggregate-action.

What does this actually mean? It means that a person can perceive an action as originating from a group, and a group can perceive actions as being directed at it. I’m sure that many exciting examples spring immediately to mind after hearing this proposition.

Group-Action, specifically, could be a perception that is unwarranted in a particular scenario, i.e. there was no aggregate of party-actions that would warrant such a perception. There may have never even been a party-action whatsoever. But as I wrote earlier, all perceptions are mis-perceptions anyway, so… Who cares? Let’s draw an arrow regardless.

Group-Perceptions

In addition to the perceptions of actions as having originated from groups, is there such a phenomenon as a collective perception? Our arrows indicate that we are modelling it, and while its manifestation may be non-physical, it is often written about. And in terms of a theory of mind, the mind itself need not exist for the theory to be concrete.

Since we’re not currently in the business of establishing objective truth, the arrows of group perception can stay too.

The Two-Body, Two-Parties-Per-Body Problem

Finally, we come to the abstract form of the scenario that I originally wanted to describe. Two bodies, each with two parties. Each party and each body acting towards various other entities and themselves. I’ve tried to limit the number of actions so that most symmetries are broken. We want to construct a diagram such that the number of possible duplicate descriptions is kept to a minimum. This was achieved mostly through intuition. I’d love to find out if there is a more rigorous way to attack such a goal.

This diagram is intended to be sufficient to represent various simple forms of both inter and intra-organizational collaboration, conflict, communication, perception, and action. The entities involved are intended to be kept to a minimum, and there should be an economy of action between those entities. This should not only allow the description of objective facts, but also present a model for the description of misunderstanding, mis-perception, miscommunication, and confusion in general, both accidental, and intentionally constructed. Note that this framework doesn’t put forward any solutions or resolutions, merely provides a descriptive language to be used in the discussions required to formulate ones own course of action:

           Body 1                  Body 2
      +--------------+        +--------------+
      |              |   A    |              |
      |              | ---------> Party 3 ---------+
      |              |        |              |   I |
      |              |   B    |      |       | <---/
+-------- Party 1 ----------> |      |       |
| G   |              |        |      |       |
\---> |      | E     |   C    |      | F     |
      |      |       | -----> |      |       |
+-----|      V       |        |      V       |-----+
| H   |              |   D    |              |   J |
\-------> Party 2  -------------> Party 4 <--------/
      |              |        |              |
      +--------------+        +--------------+
           |   ^                   |   ^
           | K |      Party 5      | L |
           +---/                   +---/

(Note: I may be able to remove actions I,J, and L after some consideration)

Analysis of

Interpretation of Actions

This totals 84 descriptions - Including duplicates.

Using the formula shown earlier: N = A * E ^ (L - 1) = 12 * (5+2) ^ (2-1) = 84.

This same scenario would lead to 588 theories of mind. That’s a hell of a lot of complexity, and this is one of the simplest inter-group scenarios possible.

That being said, the ToM angle is definitely one of the most useful in terms of resolving misunderstandings, as it is also one of the beliefs that is often most loosely held. So, how can one go about analysing such a plethora of theories-of-mind? Should one even bother to try at all? If you were to examine just a subset, how would you choose the candidates?

I suppose that the easiest approach may just be to take any particular situation at face-value until you smell something fishy, then follow your nose until you can see a path ahead that leads you to some potentially broken theories. These can then form the foundation of your investigation. Branching via connected action from party-to-party, uncovering mis-perception and observational obscurity as you go…

What’s Missing?

There’s been a lot covered in this post, so the following have had to be left out for now…

• Self action in multi-party and group scenarios
• Beyond Theory of Mind
• Concrete examples of action-entity diagrams
• Theory of mind in group dynamics
• An unambiguous language for relativistic perceptive description
• A method for generating description tables
• Automatic duplicate removal
• A formula for description-numbers sans-duplicates
• Methods of aggregation for perceived actions
• Methods of aggregation for perception of actions
• The bad-pineapple (tropical-geometry)

What’s Next?

This post has been laying the groundwork for future discussions. I’d like to take this framework and use it to analyse various contentious situations to see if there can be a better understanding of conflict, and what paths might be navigated to resolve it.

There are a lot of words written here, but hopefully I’ve kept it simple. The main take-away should be the notion of the action-entity diagram and the tabular descriptive analysis format.

Stay tuned!

Links

• Theory of Mind
• Tropical Geometry
• If a Tree Falls in a Forest
• Crow Theory of Mind - Google Scholar

Notes

• The interplay between domestic and international politics is fascinating and enlightening.
• If global actions seem bizarre, ask yourself, do you understand the domestic context?
• Respect and Value are often confused and conflated
• How to talk about conflict
• How to talk about interpretation and mis-interpretation of events, ideas, and perceptions
• Tropical Geometry of minimums and maximums
• Group Perceptions - What does it mean for a group to perceive?
• Canonical form - Observations relative to a perceiver

Appendix

Perceptive Description Table Generation

-- Haskell:

[ [y] ++ take 1 x ++ [last x] ++ " | " ++ [y] ++ " | " ++ x |
  x <- ["Group 1","Group 2","Party 1","Party 2","Party 3","Party 4","Party 5"],
  y <- "ABCDEFGHIJKL" ]